Providence looked ready from the start, dumping the ball inside Notre Dame's zone defense and pounding the offensive glass.
"I just thought we played at such a high level," Cooley said. "I just thought we played with such great confidence, and it's because of what we did defensively."
Bryce Cotton, the Big East scoring leader, had 19 points and LaDontae Henton 13 for the Friars (14-11, 6-7).
It was Providence's second win over a ranked team in 10 days following a 54-50 victory over then-No. 17 Cincinnati on Feb. 6.
"I think they are the most underrated team in our league, quite frankly," Irish coach Mike Brey said. "They're really hard to guard. I think Ed's done a fabulous job with them. I don't know if it was as much about us not playing great as it was them really playing well. When Batts is doing that inside, he's a pro. It's almost impossible to stop him."
The Friars held the Irish to 39.3 percent shooting, outrebounded them 43-32 and had 20 assists on their 29 baskets.
Notre Dame, which had played three overtime games in its previous four winning all of them continually was beat down the floor for easy baskets.
It was such an easy game for the Friars that Cooley even was joking about some bad shots by Council.
"I think he was a 3 away from a triple-double," Cooley said. "I was wondering why he kept heaving up bad shots."
Batts had 14 of his points in the opening half on 7-of-9 shooting.
"Our chemistry is great," he said. "I don't see a lot of teams that can beat us with the defense we play."